Photometric Distances for Metal-poor Giants and a Search for Hypervelocity Stars with LAMOST DR13 and Gaia DR3

Hypervelocity stars (HVSs) are stars with velocities high enough to escape the Milky Way, but their identification depends sensitively on distance estimates, particularly for distant giants. In this work, we search for metal-poor HVS candidates by combining LAMOST DR13 spectroscopy with Gaia DR3 astrometry. We calibrate a metallicity-dependent color--absolute-magnitude relation for normal metal-poor giants using a high-quality reference sample, and apply it to derive photometric distances for 41, 331 stars. The relation reproduces the reference absolute magnitudes with a scatter of 0.24,mag, corresponding to an intrinsic distance uncertainty of about 9.7%. Combining these distances with Gaia proper motions and LAMOST radial velocities, we identify 13 initially unbound candidates under the Galactic potential from. Spectral inspection indicates that several are chromospherically active binaries or other non-standard systems for which a giant-star calibration is unreliable; removing these contaminants leaves nine metal-poor HVS candidates. Backward orbit integrations suggest that one candidate is most consistent with a disk origin, while three have trajectories suggestive of an association with the Sagittarius stream.